Q. 12

# If zeros of the polynomial f (x) = x3 – 3px2 + qx – r are in A.P., thenA. 2p3 = pq – rB. 2p3 = pq + rC. p3 = pq – rD. None of these

Given;

f(x) = x3 – 3px2 + qx – r

Let a, b and c be the zeroes of the polynomial x3 – 3px2 + qx – r

a + b + c = 3 p

ab + bc + ac = q

abc = r

a + b = 2b b = p a + c = 2p

b(a + c) + ac = q

2p2 + ac = q

ac = r/p

2p2 + r/p = q

2p3 = pq – r

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